The present invention relates to a method for determining geometry data for a first bevel gear in a bevel gear drive which, in addition to the first bevel gear has a second bevel gear. The present invention furthermore relates to a bevel gear drive which has a first and a second bevel gear.
The following discussion of related art is provided to assist the reader in understanding the advantages of the invention, and is not to be construed as an admission that this related art is prior art to this invention.
A variety of gear drives exists in mechanical engineering, such as spur/cylindrical gear drives and bevel gear drives.
In the case of gear drives, two gears each rotate about their own axis of rotation. Both gears have teeth with tooth flanks via which the gears act on each other. Each tooth on the gears is in drive contact with a tooth on the other gear only during part of a rotation of the gear concerned.
If one of the gears is engaging with a particular tooth flank on one of its teeth on the other gear, it is possible that at any point in time only a point, or only a few points, on the tooth flank concerned are in contact with the other gear. This type of contact is commonly referred to in the prior art as point contact. Alternatively, it is possible that the contact concerned is made at one and the same point in time at a plurality of points on a tooth flank, where these points together form a line. This type of contact is commonly referred to in the prior art as linear contact. In the case of a linear contact, the torque which is to be transmitted from one gear to the other is distributed over a substantially greater area than in the case of a point contact. A consequence of this is a more even transmission of the force and a lower stress on the gears.
In the case of cylindrical gear drives, under optimal conditions two cylindrical gears lie in one plane and execute a rotational movement. Thus the axes of rotation are parallel to each other. The rotational movements are—depending on the nature of the cylindrical gear drive—in the same sense or in opposite senses. If one follows the movement of a pair of contact points—that is to say two points, one on the one gear and another on the other gear, which touch each other at a particular point in time—then each of the two points describes a circle in the one and same plane. The ‘interrolling’ movement can be investigated in this plane, and indeed independently of the width of the tooth. A view of this type is commonly referred to in the prior art as transverse section. Without loss of generality, a cylindrical gear drive can be investigated in a plane of this type. The problem involved is one of so-called planar kinematics.
The shape of the gears should be oriented around the interrolling action of the gear train. During the interrolling of the gears, there is contact between one tooth on each gear or between several teeth on each. Without loss of generality, it is possible to investigate the interactions between exactly one tooth on the drive input side and exactly one tooth on the drive output side. The region of a tooth which comes into contact during the interrolling is referred to below as the active flank.
For cylindrical gear drives, the conditions that the active flanks must satisfy in order to permit uninterrupted contact between the teeth in a transverse section have long been known.
If a cylindrical gear is viewed in a transverse section, then the active flank is a planar curve. This curve is referred to below as the tooth profile line. The geometric location, within the plane of investigation, at which the two tooth profile lines of the gear train contact each other, is referred to as the contact point. During the interrolling of the two gears against each other, the contact point moves along a contact path. This contact path is a characteristic contour. The planar law of gearing says that at the contact point the two tooth profile lines must have a common normal and that this normal must divide the distance between the two axes of rotation in the inverse (reciprocal) ratio to the rotational speeds. The point of intersection of the normal with the line connecting the two axes of rotation is commonly referred to as the pitch point.
The planar law of gearing establishes a direct connection, in a transverse section, between the contact path on the one hand and the tooth profile line on the other for a prescribed transmission ratio. This geometric connection can be translated into an explicit analytical calculation.
In the case of a cylindrical gear drive, the individual transverse sections can be investigated independently of one another. In particular, the planar law of gearing can also be satisfied in each transverse section. In the case of cylindrical gear drives it is therefore possible without further ado to achieve a linear contact. For the best-known solution, the so-called involute toothing, the contact path forms a straight line through the pitch point in the plane investigated.
By comparison with cylindrical gear drives, bevel gear drives have a substantially more complex interrolling geometry. A simple transference of the toothing derived for cylindrical gear drives to bevel gear drives is not possible without further considerations. In particular, bevel gear drives have two axes of rotation which intersect with each other. The angle of intersection, at which the two axes of rotation cut each other, can—within certain limits—be arbitrary. In theory and in practice the angle of intersection is often 90°. If one follows the movement of a pair of contact points, then it is true that in the case of a bevel gear drive each of these two contact points again describes a circle. However, unlike a cylindrical gear drive, these two circles do not lie in a common plane. The constant (and equal) distance from the two contact points to the point of intersection of the two axes of rotation has the consequence, however, that the two circles are located on a common spherical surface. Analogously to cylindrical gear drives, the interrolling can thus be investigated on this spherical surface independently of the tooth width. In what follows, a view of this nature will be referred to as a spherical section. Without loss of generality, the analysis can again be carried out for an infinitely thin tooth (that is, within the spherical section). One speaks of a problem of spherical kinematics.
Since the interrolling of the active flanks against each other does not represent a problem of planar kinematics, the planar law of gearing cannot be applied. The question then arises as to the arrangement of the active flanks of the bevel gears which will produce good running characteristics in the bevel gear drive.
In practice, the manufacture of bevel gears for bevel gear drives has been determined by historical developments. It is carried out using special machines and special tools, which are mainly responsible for the geometry of the bevel gear concerned. As a general rule, restrictions have applied which do not permit a free choice of the tooth forms. For example, the special machines can be subject to kinematic imperatives.
There are known theoretical considerations for the shape of bevel gear drives, which to some extent already investigate the active flanks in a spherical section.
In order to determine the geometry of the active flanks, in the prior art cited a flat countergear, a so-called planar gear, is made to interroll virtually. This planar gear has trapezoidal teeth—analogous to the involute gear teeth on cylindrical gears. One commonly refers to a trapezoidal reference profile. The toothing arrangement on the bevel gear which then results is referred to as octoidal toothing.
Furthermore, use can also be made of a simplification by which the investigation is not in the spherical section but instead on an auxiliary cone which stands orthogonally to the bevel gear. This approach is known in the prior art as Tredgold's approximation, which leads to a computational substitute toothing, by which the conditions in the contact region of the bevel gear drive are approximated by a cylindrical gear drive. The substitute cylindrical gear can thus again be investigated in individual transverse sections. Only this approximation has found its way into the practice of manufacturing technology.
In the practical manufacture of bevel gears, therefore, only an approximation is produced to the octoidal toothing known from theoretical considerations. Depending on the manufacturing process, the single and dual flank processing of a bevel gear does not lay down the profile in the spherical section, and it is not enlarged with increasing sphere radius. This results in a toothing profile which at any point in time still only has a point contact. As the trajectory of the contact point, a one-dimensional contact path is produced, the distance of which from the point of intersection of the two axes of rotation varies with the rotation of the bevel gears.
The manufacture of the active flanks by the unwinding of a spherical surface area to generate a so-called spherical involute has also already been discussed in the prior art. This approach corresponds to the geometric generation of the involute toothing of cylindrical gears by unwinding the circumference of a circle. Similar to using spherical kinematic solution approaches, the spherical involute form has however not been pursued further due to the manufacturing limitations on bevel gears.
With the present prior art, bevel gears are considered as fit to run if the law of gearing in the form of Tredgold's approximation is satisfied in a transverse section of the active flank at the instant of the interrolling. If one investigates the sequence of individual contact points during the interrolling, one obtains the contact path. However, the toothings permit only a point contact.
For optimizing the running characteristics of bevel gear drives, macro-geometry parameters of the toothing as, for example, the number of teeth, the module, tooth width, etc. have been varied in the prior art. Alternatively, settings of the basic manufacturing machinery and/or the axis parameters of a basic free-form machine can be varied. However, even when using all these optimizations, linear contact cannot be achieved.
It would therefore be desirable and advantageous to obviate prior art shortcomings and to provide an improved method and system for achieving a linear contact in a bevel gear drive when the bevel gears of the bevel gear drive interroll against each other.